ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <algorithm>
  24 #include <iostream>
  25 #include <stdexcept>
  26
  27 #include "ncmul.h"
  28 #include "ex.h"
  29 #include "add.h"
  30 #include "mul.h"
  31 #include "debugmsg.h"
  32
  33 #ifndef NO_GINAC_NAMESPACE
  34 namespace GiNaC {
  35 #endif // ndef NO_GINAC_NAMESPACE
  36
  37 //////////
  38 // default constructor, destructor, copy constructor assignment operator and helpers
  39 //////////
  40
  41 // public
  42
  43 ncmul::ncmul()
  44 {
  45     debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  46     tinfo_key = TINFO_ncmul;
  47 }
  48
  49 ncmul::~ncmul()
  50 {
  51     debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  52     destroy(0);
  53 }
  54
  55 ncmul::ncmul(ncmul const & other)
  56 {
  57     debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  58     copy(other);
  59 }
  60
  61 ncmul const & ncmul::operator=(ncmul const & other)
  62 {
  63     debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  64     if (this != &other) {
  65         destroy(1);
  66         copy(other);
  67     }
  68     return *this;
  69 }
  70
  71 // protected
  72
  73 void ncmul::copy(ncmul const & other)
  74 {
  75     exprseq::copy(other);
  76 }
  77
  78 void ncmul::destroy(bool call_parent)
  79 {
  80     if (call_parent) exprseq::destroy(call_parent);
  81 }
  82
  83 //////////
  84 // other constructors
  85 //////////
  86
  87 // public
  88
  89 ncmul::ncmul(ex const & lh, ex const & rh) :
  90     exprseq(lh,rh)
  91 {
  92     debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  93     tinfo_key = TINFO_ncmul;
  94 }
  95
  96 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
  97     exprseq(f1,f2,f3)
  98 {
  99     debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
 100     tinfo_key = TINFO_ncmul;
 101 }
 102
 103 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 104       ex const & f4) : exprseq(f1,f2,f3,f4)
 105 {
 106     debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
 107     tinfo_key = TINFO_ncmul;
 108 }
 109
 110 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 111       ex const & f4, ex const & f5) : exprseq(f1,f2,f3,f4,f5)
 112 {
 113     debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 114     tinfo_key = TINFO_ncmul;
 115 }
 116
 117 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 118       ex const & f4, ex const & f5, ex const & f6) :
 119     exprseq(f1,f2,f3,f4,f5,f6)
 120 {
 121     debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 122     tinfo_key = TINFO_ncmul;
 123 }
 124
 125 ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
 126 {
 127     debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 128     tinfo_key = TINFO_ncmul;
 129 }
 130
 131 ncmul::ncmul(exvector * vp) : exprseq(vp)
 132 {
 133     debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 134     tinfo_key = TINFO_ncmul;
 135 }
 136
 137 //////////
 138 // functions overriding virtual functions from bases classes
 139 //////////
 140
 141 // public
 142
 143 basic * ncmul::duplicate() const
 144 {
 145     debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 146     return new ncmul(*this);
 147 }
 148
 149 bool ncmul::info(unsigned inf) const
 150 {
 151     throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 152 }
 153
 154 typedef vector<int> intvector;
 155
 156 ex ncmul::expand(unsigned options) const
 157 {
 158     exvector sub_expanded_seq;
 159     intvector positions_of_adds;
 160     intvector number_of_add_operands;
 161
 162     exvector expanded_seq=expandchildren(options);
 163
 164     positions_of_adds.resize(expanded_seq.size());
 165     number_of_add_operands.resize(expanded_seq.size());
 166
 167     int number_of_adds=0;
 168     int number_of_expanded_terms=1;
 169
 170     unsigned current_position=0;
 171     exvector::const_iterator last=expanded_seq.end();
 172     for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 173         if (is_ex_exactly_of_type((*cit),add)) {
 174             positions_of_adds[number_of_adds]=current_position;
 175             add const & expanded_addref=ex_to_add(*cit);
 176             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 177             number_of_expanded_terms *= expanded_addref.seq.size();
 178             number_of_adds++;
 179         }
 180         current_position++;
 181     }
 182
 183     if (number_of_adds==0) {
 184         return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 185                                                     status_flags::expanded);
 186     }
 187
 188     exvector distrseq;
 189     distrseq.reserve(number_of_expanded_terms);
 190
 191     intvector k;
 192     k.resize(number_of_adds);
 193
 194     int l;
 195     for (l=0; l<number_of_adds; l++) {
 196         k[l]=0;
 197     }
 198
 199     while (1) {
 200         exvector term;
 201         term=expanded_seq;
 202         for (l=0; l<number_of_adds; l++) {
 203             GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 204             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 205             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 206         }
 207         distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 208                                                         status_flags::expanded));
 209
 210         // increment k[]
 211         l=number_of_adds-1;
 212         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 213             k[l]=0;
 214             l--;
 215         }
 216         if (l<0) break;
 217     }
 218
 219     return (new add(distrseq))->setflag(status_flags::dynallocated |
 220                                         status_flags::expanded);
 221 }
 222
 223 int ncmul::degree(symbol const & s) const
 224 {
 225     int deg_sum=0;
 226     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 227         deg_sum+=(*cit).degree(s);
 228     }
 229     return deg_sum;
 230 }
 231
 232 int ncmul::ldegree(symbol const & s) const
 233 {
 234     int deg_sum=0;
 235     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 236         deg_sum+=(*cit).ldegree(s);
 237     }
 238     return deg_sum;
 239 }
 240
 241 ex ncmul::coeff(symbol const & s, int const n) const
 242 {
 243     exvector coeffseq;
 244     coeffseq.reserve(seq.size());
 245
 246     if (n==0) {
 247         // product of individual coeffs
 248         // if a non-zero power of s is found, the resulting product will be 0
 249         exvector::const_iterator it=seq.begin();
 250         while (it!=seq.end()) {
 251             coeffseq.push_back((*it).coeff(s,n));
 252             ++it;
 253         }
 254         return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 255     }
 256
 257     exvector::const_iterator it=seq.begin();
 258     bool coeff_found=0;
 259     while (it!=seq.end()) {
 260         ex c=(*it).coeff(s,n);
 261         if (!c.is_zero()) {
 262             coeffseq.push_back(c);
 263             coeff_found=1;
 264         } else {
 265             coeffseq.push_back(*it);
 266         }
 267         ++it;
 268     }
 269
 270     if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 271
 272     return exZERO();
 273 }
 274
 275 unsigned ncmul::count_factors(ex const & e) const
 276 {
 277     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 278         (is_ex_exactly_of_type(e,ncmul))) {
 279         unsigned factors=0;
 280         for (int i=0; i<e.nops(); i++) {
 281             factors += count_factors(e.op(i));
 282         }
 283         return factors;
 284     }
 285     return 1;
 286 }
 287
 288 void ncmul::append_factors(exvector & v, ex const & e) const
 289 {
 290     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 291         (is_ex_exactly_of_type(e,ncmul))) {
 292         for (int i=0; i<e.nops(); i++) {
 293             append_factors(v,e.op(i));
 294         }
 295         return;
 296     }
 297     v.push_back(e);
 298 }
 299
 300 typedef vector<unsigned> unsignedvector;
 301 typedef vector<exvector> exvectorvector;
 302
 303 ex ncmul::eval(int level) const
 304 {
 305     // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 306     //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 307     //                  ncmul(x) -> x
 308     //                  ncmul() -> 1
 309     //                  ncmul(...,c1,...,c2,...) ->
 310     //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 311     //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 312     //                      (collect elements of same type)
 313     //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 314     // the following rule would be nice, but produces a recursion,
 315     // which must be trapped by introducing a flag that the sub-ncmuls()
 316     // are already evaluated (maybe later...)
 317     //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 318     //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 319     //                      (X noncommutative_composite)
 320
 321     if ((level==1)&&(flags & status_flags::evaluated)) {
 322         return *this;
 323     }
 324
 325     exvector evaledseq=evalchildren(level);
 326
 327     // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 328     //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 329     unsigned factors=0;
 330     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 331         factors += count_factors(*cit);
 332     }
 333
 334     exvector assocseq;
 335     assocseq.reserve(factors);
 336     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 337         append_factors(assocseq,*cit);
 338     }
 339
 340     // ncmul(x) -> x
 341     if (assocseq.size()==1) return *(seq.begin());
 342
 343     // ncmul() -> 1
 344     if (assocseq.size()==0) return exONE();
 345
 346     // determine return types
 347     unsignedvector rettypes;
 348     rettypes.reserve(assocseq.size());
 349     unsigned i=0;
 350     unsigned count_commutative=0;
 351     unsigned count_noncommutative=0;
 352     unsigned count_noncommutative_composite=0;
 353     for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 354         switch (rettypes[i]=(*cit).return_type()) {
 355         case return_types::commutative:
 356             count_commutative++;
 357             break;
 358         case return_types::noncommutative:
 359             count_noncommutative++;
 360             break;
 361         case return_types::noncommutative_composite:
 362             count_noncommutative_composite++;
 363             break;
 364         default:
 365             throw(std::logic_error("ncmul::eval(): invalid return type"));
 366         }
 367         ++i;
 368     }
 369     GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 370
 371     // ncmul(...,c1,...,c2,...) ->
 372     //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 373     if (count_commutative!=0) {
 374         exvector commutativeseq;
 375         commutativeseq.reserve(count_commutative+1);
 376         exvector noncommutativeseq;
 377         noncommutativeseq.reserve(assocseq.size()-count_commutative);
 378         for (i=0; i<assocseq.size(); ++i) {
 379             if (rettypes[i]==return_types::commutative) {
 380                 commutativeseq.push_back(assocseq[i]);
 381             } else {
 382                 noncommutativeseq.push_back(assocseq[i]);
 383             }
 384         }
 385         commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 386                                   setflag(status_flags::dynallocated));
 387         return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 388     }
 389
 390     // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 391     //     (collect elements of same type)
 392
 393     if (count_noncommutative_composite==0) {
 394         // there are neither commutative nor noncommutative_composite
 395         // elements in assocseq
 396         GINAC_ASSERT(count_commutative==0);
 397
 398         exvectorvector evv;
 399         unsignedvector rttinfos;
 400         evv.reserve(assocseq.size());
 401         rttinfos.reserve(assocseq.size());
 402
 403         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 404             unsigned ti=(*cit).return_type_tinfo();
 405             // search type in vector of known types
 406             for (i=0; i<rttinfos.size(); ++i) {
 407                 if (ti==rttinfos[i]) {
 408                     evv[i].push_back(*cit);
 409                     break;
 410                 }
 411             }
 412             if (i>=rttinfos.size()) {
 413                 // new type
 414                 rttinfos.push_back(ti);
 415                 evv.push_back(exvector());
 416                 (*(evv.end()-1)).reserve(assocseq.size());
 417                 (*(evv.end()-1)).push_back(*cit);
 418             }
 419         }
 420
 421 #ifdef DO_GINAC_ASSERT
 422         GINAC_ASSERT(evv.size()==rttinfos.size());
 423         GINAC_ASSERT(evv.size()>0);
 424         unsigned s=0;
 425         for (i=0; i<evv.size(); ++i) {
 426             s += evv[i].size();
 427         }
 428         GINAC_ASSERT(s==assocseq.size());
 429 #endif // def DO_GINAC_ASSERT
 430
 431         // if all elements are of same type, simplify the string
 432         if (evv.size()==1) {
 433             return evv[0][0].simplify_ncmul(evv[0]);
 434         }
 435
 436         exvector splitseq;
 437         splitseq.reserve(evv.size());
 438         for (i=0; i<evv.size(); ++i) {
 439             splitseq.push_back((new ncmul(evv[i]))->
 440                                setflag(status_flags::dynallocated));
 441         }
 442
 443         return (new mul(splitseq))->setflag(status_flags::dynallocated);
 444     }
 445
 446     return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 447                                           status_flags::evaluated);
 448 }
 449
 450 exvector ncmul::get_indices(void) const
 451 {
 452     // return union of indices of factors
 453     exvector iv;
 454     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 455         exvector subiv=(*cit).get_indices();
 456         iv.reserve(iv.size()+subiv.size());
 457         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 458             iv.push_back(*cit2);
 459         }
 460     }
 461     return iv;
 462 }
 463
 464 ex ncmul::subs(lst const & ls, lst const & lr) const
 465 {
 466     return ncmul(subschildren(ls, lr));
 467 }
 468
 469 ex ncmul::thisexprseq(exvector const & v) const
 470 {
 471     return (new ncmul(v))->setflag(status_flags::dynallocated);
 472 }
 473
 474 ex ncmul::thisexprseq(exvector * vp) const
 475 {
 476     return (new ncmul(vp))->setflag(status_flags::dynallocated);
 477 }
 478
 479 // protected
 480
 481 int ncmul::compare_same_type(basic const & other) const
 482 {
 483     return exprseq::compare_same_type(other);
 484 }
 485
 486 unsigned ncmul::return_type(void) const
 487 {
 488     if (seq.size()==0) {
 489         // ncmul without factors: should not happen, but commutes
 490         return return_types::commutative;
 491     }
 492
 493     bool all_commutative=1;
 494     unsigned rt;
 495     exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 496
 497     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 498         rt=(*cit).return_type();
 499         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 500         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 501             // first nc element found, remember position
 502             cit_noncommutative_element=cit;
 503             all_commutative=0;
 504         }
 505         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 506             // another nc element found, compare type_infos
 507             if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 508                 // diffent types -> mul is ncc
 509                 return return_types::noncommutative_composite;
 510             }
 511         }
 512     }
 513     // all factors checked
 514     GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 515     return all_commutative ? return_types::commutative : return_types::noncommutative;
 516 }
 517
 518 unsigned ncmul::return_type_tinfo(void) const
 519 {
 520     if (seq.size()==0) {
 521         // mul without factors: should not happen
 522         return tinfo_key;
 523     }
 524     // return type_info of first noncommutative element
 525     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 526         if ((*cit).return_type()==return_types::noncommutative) {
 527             return (*cit).return_type_tinfo();
 528         }
 529     }
 530     // no noncommutative element found, should not happen
 531     return tinfo_key;
 532 }
 533
 534 //////////
 535 // new virtual functions which can be overridden by derived classes
 536 //////////
 537
 538 // none
 539
 540 //////////
 541 // non-virtual functions in this class
 542 //////////
 543
 544 exvector ncmul::expandchildren(unsigned options) const
 545 {
 546     exvector s;
 547     s.reserve(seq.size());
 548
 549     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 550         s.push_back((*it).expand(options));
 551     }
 552     return s;
 553 }
 554
 555 exvector const & ncmul::get_factors(void) const
 556 {
 557     return seq;
 558 }
 559
 560 //////////
 561 // static member variables
 562 //////////
 563
 564 // protected
 565
 566 unsigned ncmul::precedence=50;
 567
 568
 569 //////////
 570 // global constants
 571 //////////
 572
 573 const ncmul some_ncmul;
 574 type_info const & typeid_ncmul=typeid(some_ncmul);
 575
 576 //////////
 577 // friend functions
 578 //////////
 579
 580 ex nonsimplified_ncmul(exvector const & v)
 581 {
 582     return (new ncmul(v))->setflag(status_flags::dynallocated);
 583 }
 584
 585 ex simplified_ncmul(exvector const & v)
 586 {
 587     if (v.size()==0) {
 588         return exONE();
 589     } else if (v.size()==1) {
 590         return v[0];
 591     }
 592     return (new ncmul(v))->setflag(status_flags::dynallocated |
 593                                    status_flags::evaluated);
 594 }
 595
 596 #ifndef NO_GINAC_NAMESPACE
 597 } // namespace GiNaC
 598 #endif // ndef NO_GINAC_NAMESPACE